Cosmetic rust is nothing more than unsightly as long as the chain still tests within length limits. Like others have said, just oil it and go. It's not going to hurt anything. It's not the end of the world.

Use the ruler test to make sure the chain isn't out of spec and check to see if your cogs/chainwheels are not too worn. A good investment is a Park Tool chain gauge which takes the guesswork out of checking a chain and doesn't require crawling around on your knees or putting the bike up on a stand to quickly check your chain's condition. It's a quick go/no-go slap-on gauge that takes 10 seconds to use.

Running a worn-out "stretched" chain will damage your cogs and chainwheels in a hurry so you want to keep an eye on that. Rust on the outside of the chain isn't going to hurt anything though.

In the end chains are cheap disposable wear items that you'll go through rather quickly if you ride a lot. Many people go nuts with fancy nostrum snake oils and lubricaion crap and spend way more money trying to get an extra tiny bit of life out of what is a $10-15 disposable item (unless of course you are riding a recumbent or tandem with 152 feet of chain on it.) Throw some oil on it every once in a while and let it go until it's time to replace it with a new one because of "stretch" wear. If you buy a chain online it's not any bigger of a deal than replacing a tube or a tyre.

Any old oil will do that doesn't make too much of a mess.